No, a DISboards group is not a FB group. They are separate entities. Yes, people can start on one, and migrate to the other, but they are separate. Even if one person is on both sites, they are participating in two different groups, not the same one.
My first Fish Extender experience, I was on two different cruise boards, DIS being one of them. Each group had a FE group. There were several people who were on both forums, and some of them were in both FE groups. There were others on each forum that only participated in that particular forum's group and only did the FE on that forum.
No reason that DIS and FB (as well as any other social site who wants to start a group) can't have each have their own.
But, to say that the DISboards Fish Extender group is on FB is not correct.
My first experience with Cruise Meet groups, we had a super active group, and set up all sorts of activities for the cruise, including a Fish Extender group. But, all cruise activity related discussion were only on DISboards. If people in the cruise meet group wanted to participate in private discussions (how're the kids?/ We had our house painted/Oh, wow, I also grew up in XXX), they did so via FB.
It worked great that way.
For those people who love FB, more power to them. But, please, don't keep lecturing me about how great FB is. I have no interest in joining it, or participating over there. I like our group here on DISboards.